Higher Prelim Topic Revision

1 Straight Line

Perpendicular bisectors pass through the midpoint of a line segment, and run perpendicular to them.

\(4y=-3x+29\) or \(y=-\frac{3}{4}x+\frac{29}{2}\)

For more practice, try: Zeta Higher Textbook, Page 15, Exercise 1.8, Questions 1(a), 1(b) and 1(c)

A straight line equation must be rearranged to make \(y\) the subject (\(y=\dots\)) before its gradient can be determined.

\(2y=-x-5\) or \(y=-\frac{1}{2}x-\frac{5}{2}\)

For more practice, try: Zeta Higher Textbook, Page 13, Exercise 1.6, Questions 3, 4 and 5

The formula \(m=\tan{\theta}\) links a line's gradient to the angle it makes with the positive direction of the \(x\)-axis.

\(y=-x+2\)

For more practice, try: Zeta Higher Textbook, Page 9, Exercise 1.4A, Questions 1, 2 and 3

Calculate the gradients of PQ and QR first. The conclusion to a collinearity problem needs to be learned carefully.

\(m_{PQ}=m_{QR}=-3\), valid statement

For more practice, try: Zeta Higher Textbook, Page 12, Exercise 1.5, Questions 1(a), 1(b) and 1(c)

Medians meet opposite sides at the midpoint.
Altitudes meet opposite sides at an angle of 90 degrees.
You can use \(y=y\) as a first step to finding points of intersection.

\(y=-3x+5\)
\(2y=-x-5\) or \(y=-\frac{1}{2}x-\frac{5}{2}\)
\((3,-4)\)

For more practice, try: Zeta Higher Textbook, Page 21, Exercise 1.11B, Questions 1, 2 and 3

2 Recurrence Relations

Calculate \(u_1\) first using the value of \(u_0\) as a starting point.
What is the value of \(a\)?

What is the formula for the limit of a recurrence relation?

\(15\)
\(-1<a<1\), valid statement

\(9\)

For more practice, try: Zeta Higher Textbook, Page 90, Exercise 6.1, Questions 1(a), 1(b) and 1(c)

Can you put both \(u_2\) and \(u_3\) into the recurrence relation? Where does each one go?
What is the value of \(a\)?

\(-4\)
\(a>1\), valid statement

For more practice, try: Zeta Higher Textbook, Page 93, Exercise 6.3, Questions 1(f), 1(i) and 1(l)

Substitute the value of \(u_4\) into the recurrence relation.
Use your expression from part (a), and the new information that \(u_5=-1\).

\(6k-4\)
\(k=\frac{1}{2}\)

For more practice, try: Zeta Higher Textbook, Page 15, Exercise 1.8, Questions 1(a), 1(b) and 1(c)

What "12% is subtracted (from the original 100%) as a decimal?
Since dividing by \(0.12\) is tricky, multiply both parts of the fraction by \(100\) and work from there.

\(a=0.88,b-30\)
250 squirrels

For more practice, try: Zeta Higher Textbook, Page 96, Exercise 6.5B, Questions 1, 2 and 3

Create two equations: one linking the first two terms, and a second linking the second term and the third term. Solve simultaneously.

\(p=-\frac{1}{2},q=2\)

For more practice, try: Zeta Higher Textbook, Page 91, Exercise 6.2, Questions 1(a), 1(b) and 1(c)

3 Differentiation I

Coming soon.

4 Quadratic Theory

Coming soon.

5 Sets and Functions

Coming soon.

Start by using a formula to find the gradient between the points.Coming soon.

Coming soon.

6 Trigonometry

Coming soon.

7 Graph Transformations

Coming soon.

8 Vectors

Coming soon.

9 Differentiation II

Coming soon.

10 Polynomials

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11 Integration

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12 Addition Formulae

Coming soon.

TComing soon.

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13 The Circle

Coming soon.

Higher Prelim Topic Revision - Web Version

1 Straight Line

2 Recurrence Relations

3 Differentiation I

4 Quadratic Theory

5 Sets and Functions

6 Trigonometry

7 Graph Transformations

8 Vectors

9 Differentiation II

10 Polynomials

11 Integration

12 Addition Formulae

13 The Circle